LabsFall2008 - AS103 Descriptive Astronomy Laboratory...

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Unformatted text preview: AS103 - Descriptive Astronomy Laboratory Materials Fall 2008 NOTE: When printing these labs in preparation for class, pay attention to the name of the lab in the footer to make sure you print all the pages. This document is not paginated for double-sided printing. Fall 2008 1 AS103 - Descriptive Astronomy Lab 1: TheSky Workbook – Fall 2008 I: Introduction TheSky Workbook is purchased at the bookstore and contains TheSky Astronomy Software in a package at the back of the book. This software is currently available on the school’s network (to a very limited extent) at the second floor computer lab in the Applied Technology Building (ATC). This lab has 15 computers running this software. It is best if you can install the software on your own computer. It will run under the Windows or Mac operating systems. Once you have installed the software, you need to work your way through this workbook. This should be done at home or if you have a laptop, anywhere you please. Those who have a laptop have the advantage of bringing the computer with them if they have a question about the software or the workbook. Chapter 1 of the workbook includes complete instructions on the installation of the software. It does not show instructions for installing the software on a Mac, but students have done so successfully. This chapter also shows you how to set the correct Earth location and time zone information. Note carefully the instructions for setting up the multimedia folder, as this will become important in later chapters. If you have trouble with this part, I will eventually place the needed files on Blackboard. Chapter 2 introduces you to using the software toolbars and shortcuts. Chapter 3 explains how to set your location and time, allowing you to view the sky from different locations on Earth and at different times, running from thousands of years in the past to thousands of years into the future. Chapter 4 explains how to find the names of objects in the sky and some history behind those names. Most objects have many names, or catalog numbers. Chapter 5 is a tutorial for finding objects based on celestial coordinate systems. (We will see some of these ideas in the in-class lab activities as well.) Chapter 6 shows you the motions of the sky at the various horizon directions and at different locations throughout the world. Understanding these motions allows us to understand the majority of astronomer’s work during the first 600 years or so of history. These motions are responsible for the rhythms of our daily lives – from keeping time to sailing ships. The seven days of the week are derived from these motions. Chapter 7 is about keeping time. Astronomy uses several methods for keeping time. Chapter 8 tells about the seasons – the solstices and the equinoxes. Chapter 9 is about phases of the Moon and eclipses. There are many other useful tools in the program which you will learn about as you go through the workbook. II: Your Responsibilities You are required to go through the entire workbook during the semester. You are free to do this at your own pace, but remember there is a due date. There is a customized worksheet associated with this workbook. The worksheet is due on Thursday, 4 Dec 2008, at 3:00PM. Note: Feel free to turn your work in early. The worksheet is not accepted late – for any reason what-so-ever. You have three months to do this work. Get it done. Fall 2008 TheSky Workbook 2 I II: Grading Because the workbook answers can be easily copied from other students (which has happened) the workbooks are not turned in for credit. The worksheet is customized for each student. The questions are similar but the details are different. You can not copy answers from each other – you each have different answers. Because this worksheet is customized for each of you, it is not posted to Blackboard or any other mass distribution method. You must obtain the worksheet directly from me. Because the enrollment changes during the first few weeks of the semester, I will create the worksheet and announce in class when it is available. In the mean time, you can get started with the workbook. This worksheet is valued at 400 points. Fall 2008 TheSky Workbook 3 AS103 - Descriptive Astronomy Lab 2: Coordinate Systems and Stars – Fall 2008 Due Date: Day Performed Name Lecture Section Partner Score / 40 Partner Note1: I will be in the lab classroom to answer your questions while you work on this lab. However, if you ask me a question that makes it appear that you did not read the instructions, all I will tell you is, “go read the instructions...” Note2: Any term shown in bold is a term you are responsible for knowing and could show up on the lecture test. I: Part I - Celestial Coordinates Telling someone to look for an object within a constellation is one way of expressing the location of the object in the sky. However, telling someone “Joe’s Grill” is in Pennsylvania conveys as much information as telling them NGC2566 is in Puppis. To specify the location of an object more precisely – for instance, when we want to use a telescope – we need to use a coordinate system. A coordinate system (of the type used in astronomy) uses two numbers to describe the location of an object, by stating the distance of the object from the coordinate system’s starting point. The location of the starting point must be known and agreed to by all observers. The object’s location is specified by measuring along two perpendicular reference lines, from the starting point to the object. In all of these coordinate systems, the measurements to the position of an object are measurements of angles. The angles are measured in units of degrees, minutes and seconds. This system should already be familiar to you as a student. To remind you, there are 360 degrees (symbol, 360◦) in a circle, 60 minutes in a degree (symbol, 60 ) and 60 seconds (symbol, 60 ) in a minute. If the angle is written as degrees, minutes and seconds, it may be shown as: 25◦ 34 14 . Also, an angle of 90◦ is called a right angle and an angle of 180◦ is called a straight angle. II: Coordinate Systems 1 There are five coordinate systems used by astronomers. We will use three (actually, 2 2 of those five, and look at a trivial situation for converting between them. The first is the horizon coordinate system and the second is the equatorial system. The Horizon Coordinate System The horizon coordinate system (Figure 2-1) uses altitude and azimuth to specify the location of an object. Both numbers are angles, measured in degrees. The altitude of an object is an angle measured from the horizon to the object. The altitude of the horizon is zero degrees (0◦ ). The point straight over your head is at altitude 90◦. Altitude angles for all objects above the horizon run between 0◦ and 90◦. Altitudes can never be greater than 90◦. If the altitude of an object is negative, the object is below the observer’s horizon. Fall 2008 Coordinate Systems and Stars 4 lM er an idi Almucantar Lo c a Altitude = +90º (Zenith) Alt itud Horizon North 0º e=0º Azimuth East 90º tim er idi an South 180º Altitude West 270º An Nadir (-90º) Figure 2-1: The horizon coordinate system. The altitude is measured with a quadrant. Figure 2-2 shows an inexpensive quadrant made with a ruler, a protractor, a piece of string and a small weight. You can use a quadrant like this to measure altitudes during your sky observations. Alternatively, an observer could use an outstretched hand to obtain a rough measure of altitudes. If the index finger is held at arm’s length, it is about two degrees across. A fist is about ten degrees across and when the fingers are spread out, there is about twenty degrees between the finger tips. Remember to hold your hand at arm’s length. Star Ruler 0 90 Protractor String Small Weight Eyeball Figure 2-2: A simple quadrant. The azimuth coordinate specifies the location on the horizon from which the altitude of the object is measured. Like altitude, azimuth is also measured as an angle. Due north is 0◦ azimuth. East is 90◦, south is 180◦ and west is 270◦. Thus, azimuth runs from 0◦ to 360◦. The main problem with the horizon system is that it depends on the time, date and location of the observation. This happens because the sky is in motion (actually, the Earth is moving, but at this point this makes no difference) and each Earthbound observer has his or her own horizon. Since the correct altitude and azimuth depends on these data, an observer using the horizon system must record the date, time and location as part of an observation. If the observer fails to record these data, the altitude and azimuth coordinates are meaningless. Since the sky appears to move, the altitude and azimuth of a star or constellation are changing from minute to minute. This problem is created by using a system starting point fixed to the Earth – the northern horizon. A Few More Terms from the Horizon System You should know a few more horizon system terms for our future discussions. For a graphic representation of these terms, see Figure 2-1. The zenith is the point in the sky directly above the observer’s position on Earth, or above the observer’s head. Each observer has their own zenith. If we draw a sky line from the northern horizon (0◦ azimuth), through the zenith, to the southern horizon (180◦ azimuth), we have drawn the local meridian. The local meridian Fall 2008 Coordinate Systems and Stars 5 is a sky line drawn from the North through the zenith to the South. Because each observer has their own zenith, each observer also has their own local meridian. The sky point directly below an observer (on the other side of the Earth) is called the nadir. The line drawn from the north through the nadir to the south is called the antimeridian. III: The Equatorial Coordinate System The preferred coordinate system among astronomers is the equatorial coordinate system. Unlike the horizon system, the equatorial system is independent of observation time, date and observer location. This independence is due to using a coordinate system starting point fixed to the sky. Thus, this system moves with the objects in the sky. The reference lines we use to guide our measurements from the starting point to an object, also move with the sky. The equatorial system is very similar to the latitude-longitude (terrestrial) system used to specify locations on Earth (the terrestrial coordinate system). Therefore, a review of the terrestrial coordinate system might make it easier to understand the celestial equatorial coordinate system. The Terrestrial Coordinate System We measure both latitude and longitude as angles. The vertexes of these angles are at the center of the Earth. On the surface of the Earth, a difference of one degree, one minute and one second of latitude is about 111 kilometers, 1,855 meters and 30.9 meters, respectively. As an example, let us use the latitude and longitude of Grand Rapids, Michigan. Grand Rapids is a big place, so we will not get excessively accurate by using minutes and seconds in this example. The latitude of Grand Rapids is 43◦ north (43◦N). Latitude is a measure of distance – in degrees, either north or south – from the Earth’s equator. Here is a way to picture the creation of this angle. Draw a line from Grand Rapids to the center of the Earth. Draw another line from the center of the Earth to a point on the equator directly south of Grand Rapids. The angle between these two lines is 43◦ , see Figure 2-3. North Pole Greenwich England 43ºN Prime Meridian Center 86ºW Equator Figure 2-3: The latitude and longitude of Grand Rapids. We can draw guidelines of equal latitude on the surface of the Earth. When looking at a globe, we can see these equal latitude lines running east-west, parallel to the equator. Since they are parallel to the equator, we sometimes call Fall 2008 Coordinate Systems and Stars 6 them parallels, such as “the 45th Parallel.” These east-west lines measure the north-south angle between themselves and the equator. This east-west, north-south relation sometimes confuses people. To understand this, stand a ruler on end as if to measure height above a table. Notice the lines drawn on the ruler are parallel with the surface of the table. The relationship between the east-west latitude lines measuring a north-south angle is the same as for the ruler lines measuring height above the table. The latitude of the equator is 0◦ and the latitude of the North Pole is 90◦ N. The South Pole’s latitude is 90◦ S. Latitude angles are never greater than 90◦. In the northern hemisphere, (all places north of the equator) there is an easy way to determine your latitude – simply measure the altitude of the North Star, Polaris. The altitude is measured with a quadrant. Polaris is (almost) directly above the North Pole. At all points in the northern hemisphere, the altitude of the North Star (Polaris) is equal to your latitude. In Grand Rapids, the altitude of Polaris is 43◦. You can use this fact to check the accuracy of your quadrant. To help remember the relationship between the altitude of Polaris and the latitude of your location, just switch the first two letters of the words: la titude and al titude. Longitude is a little more difficult than latitude. The Earth has no natural dividing line between east and west, like the equator divides north and south. We had to agree upon an east-west dividing line. At one time, French sailors divided east and west by passing a line through Paris. English sailors used London. About 200 hundred years ago, they agreed to draw a line from the North Pole, through the Royal Observatory in Greenwich, England, through the equator (at a right angle), to the South Pole. The prime meridian is the internationally recognized east-west dividing line. Greenwich, England is on the Thames River, about 16 kilometers east of London. Longitude measures the distance along the equator, from its intersection with the prime meridian, to the point on the equator from where the location’s latitude is measured. We call all locations west of the prime meridian “west longitude,” and all locations east, “east longitude.” Grand Rapids is at 86◦ west longitude (86◦ W). An Earth globe also has longitudinal lines running from the North Pole to the South Pole. Longitude runs from 0◦ to 180◦ west, and from 0◦ to 180◦ east. The line on the opposite side of the Earth from the prime meridian is the International Date Line. When it is high noon in Greenwich, England, it is midnight on the International Date Line and thus, the calendar date is changing. The Celestial Sphere We might imagine drawing lines in the sky to act like the guides we drew on the Earth globe for latitude and longitude. This crystalline, celestial sphere does not actually exist. However, we can use the concept of the celestial sphere to draw celestial latitude and longitude lines. The equivalents of latitude and longitude on the celestial sphere are called, declination and right ascension. The lines of declination and right ascension form the celestial sphere’s, equatorial coordinate system. The celestial sphere has two important points and two important lines. The two points are the north celestial pole (NCP) and the south celestial pole (SCP). The north celestial pole is a point directly above the Earth’s North Pole. The south celestial pole is a point directly above the Earth’s South Pole. The Earth rotates on its axis once every 24 hours. If we run a thin rod through the Earth such that it would rotate about this rod, then the rod also passes directly through the celestial sphere at its north and south poles. Instead of rotating the Earth, we could allow the celestial sphere to rotate on this rod. The resulting sky motions, as seen from the Earth, are the same. The celestial sphere has an equator directly above the Earth’s equator. Like the Earth’s equator, the celestial equator is a line located half way between the NCP and SCP. The celestial sphere also has a “prime meridian.” However, on the celestial sphere this line is called the zero hour (0h, 0 hour) line, which is also called the equinoctial colure. The zero hour line starts at the NCP and passes through the celestial equator at a point called the vernal equinox, down to the SCP. Equatorial Coordinates: Declination Declination is to the celestial sphere what latitude is to the Earth. Declination measures the angular distance of an object from the celestial equator. Latitude uses north (N) or south (S) to designate a position north or south of Earth’s equator. Declination uses plus (+) or minus (−) to designate a position above or below the celestial equator. On Earth, a place is at “latitude 25◦ N.” On the celestial sphere, an object is at “declination +25◦ .” The celestial Fall 2008 Coordinate Systems and Stars 7 equator is 0◦ declination, the NCP is +90◦ declination and the SCP is −90◦ declination. We can draw imaginary declination guidelines on the celestial sphere. In the sky, they run east to west, parallel to the celestial equator. These are the celestial sphere’s “parallels.” On the SC001 Constellation Chart, declination coordinate markings are printed along the edges and the important right ascension hour lines. On this chart, declination only reaches +60◦ or −60◦ , because the polar regions would be too distorted if they were plotted along the top and bottom. It is an effect similar to a rectangular map of the World, where Antarctica is spread out over the bottom of the map. This chart is called an equatorial chart because the declination coordinate is limited to this range around the celestial equator. The north-polar region of the sky is plotted on the SC2 Polar Chart. Polar charts use a different mapping technique from equatorial charts, to preserve the shape of the constellations. Notice the SC2 Polar Chart does not attempt to plot constellations close to the celestial equator. Equatorial Coordinates: Right Ascension The celestial equivalent of longitude is right ascension. When looking at the northern horizon, the stars ascend into the sky on the right. Right ascension is measured hours, minutes and seconds, like a clock. The right ascension coordinate of an object tells observers when (at what time) an object lies on their local meridian. In these units, right ascension runs from 0hr 0m 0s to 23hr 59m 59s . This is a 24-hour clock where 24hr equals 0hr . The zero hour line (the equinoctial colure) passes through the celestial equator at the vernal equinox. The vernal equinox is the starting point for the equatorial coordinate system. When your “right ascension clock” reads 0hr 0m 0s , the vernal equinox is on your local meridian. A clock that keeps track of right ascension – a sidereal clock – is different from the wall clock that runs our daily routine. A sidereal clock keeps sidereal time. “Sidereal” is a Latin word meaning, “with reference to the stars.” Thus, a sidereal clock keeps time with reference to the stars. A wall clock keeps solar time. “Solar” means “with reference to Sol.” The difference is due to the apparent annual motion of the Sun. This apparent motion is due to the actual annual revolution of the Earth around the Sun. The coordinates of the vernal equinox are, RA = 0hr 0m 0s , Dec = 0◦ 0 0 . When the vernal equinox is on your local meridian, your sidereal clock reads “stellar midnight.” Since all observers have their own zenith and local meridian, they must also have their own sidereal clock. Each observer’s sidereal clock must be set to the local sidereal time. The correct local sidereal time can be calculated from the reading of a solar clock, the date and the observer’s longitude. (TheSky program does this for you.) Other examples of right ascension coordinates are: the autumnal equinox (or the fall equinox), RA = 12hr 0m 0s , Dec = 0◦ 0 0 ; the summer solstice, RA = 6hr 0m 0s , Dec = 23◦ 30 0 ; the belt of Orion: RA ≈ 5hr 30m . This means the belt of Orion passes through the local meridian approximately 5 hours and 30 minutes after the vernal equinox passes through. On the SC001 chart, the right ascension coordinate is printed in three places – along the top, along the celestial equator and along the bottom. Since sidereal (right ascension) clocks and wall (solar) clocks are different, the vernal equinox can pass through your local meridian anytime of day. On the first day of Spring, the Sun is on the vernal equinox, so the vernal equinox passes through your local meridian at high noon. On the first day of Fall, the Sun is on the autumnal equinox (180◦ or 12 hours away from the vernal equinox), so the vernal equinox passes through your local meridian at midnight. The equatorial system has a big advantage over the horizon system. Each sky object always has the same declination and right ascension. The equatorial coordinates of an object are independent of the observer’s location, and the date and time of the observation. For any observer at any location on Earth, the right ascension and declination coordinates of any object are the same during the observer’s lifetime. Celestial Longitude Another coordinate system used by planetary astronomers is the ecliptic system. One coordinate of this system is celestial longitude. It spans 0◦ to 360◦ running along the ecliptic line (look at the degree marks along the ecliptic line on the SC001 chart). We use this coordinate occasionally for the positions of the Sun and Moon. Zero degrees celestial longitude is in the center of the SC001 chart, at the vernal equinox. Fall 2008 Coordinate Systems and Stars 8 A Small Problem Although the equatorial system is extremely accurate, it does have one problem. The right ascension and declination of an object are not quite constant. By naked eye, changes in star coordinates from night to night, season to season or even over a lifetime, can not be perceived. They do change however, over decades, centuries and millennia. It takes 72 years for the right ascension coordinate of an object along the celestial equator to change by one degree. Modern, highly accurate, computer-controlled telescopes can detect this change in right ascension in a matter of months. At the top of a typical star or constellation chart is a subtitle such as, “Epoch 1950” or “Epoch 2000.0.” This means the equatorial coordinates of the objects on the chart are adjusted for that particular year. This adjustment is necessary because of the precessional motion of the Earth. The first part of this exercise is to locate a few sky objects and locations on the chart to start to become familiar with these celestial coordinates. The first row of Table 1 is shown as an example. Some of the stars are labeled by their Greek letter (Bayer) designations (e.g. β Leonis). In these cases, use the Greek letter with the genitive form of the constellation’s name to label the star. (See the appendix in the textbook.) Complete tables 1 and 2 below. IV: The SC001 and SC002 Constellation Charts The SC001 Constellation Chart shows the stars located within 60◦ declination of the celestial equator (the line dividing upper and lower halves of the chart). This is a line in the sky which is directly above the Earth’s equator. The coordinate that measures above and below the celestial equator is called declination (Dec, or δ ). Declination is measured in degrees, with positive values above the celestial equator and negative values below. (See Figure 2-4.) The coordinate that measures from left (east) to right (west) are called right ascension (RA, or α). Right ascension is measured in hours, minutes and seconds, starting from the center of the chart, the vernal equinox. Notice that right ascension increases to the left (east). This is because objects rise in the east as the Earth turns on its axis and time passes. (See Figure 2-5.) These two coordinates are combined to specify any location or object in the sky. (See Figure 2-6.) EQUATORIAL CHART +60° +30° +30° Declination +60° Celestial Equator 0° 0° -30° -30° -60° -60° Figure 2-4: Declination on the SC001 sky chart. EQUATORIAL CHART Celestial Equator Vernal Equinox West East ks Mar Degree ks Mar Date Ecliptic Right Ascension 12 h 6 h 0 h 18 h 12 h Figure 2-5: Right ascension on the SC001 sky chart. Fall 2008 Coordinate Systems and Stars 9 D NCP ec an idi er M Decli nati o n Equinoctal Colure NP Ri g ht A s Prime Meridian Sun Equator r ato Equ stial Cele cens ion Vernal Equinox Ecliptic SCP Figure 2-6: Right ascension and declination are used to map the sky. There is a “wavy line” that also passes through the central region of the chart. This is the ecliptic line. It represents the apparent path of the Sun against the background stars (or constellations) as we orbit around it. The constellations through which the ecliptic passes are called the zodiac constellations. There are four special points along the ecliptic that are related to the seasons. Look at Figure 2-7. In the northern hemisphere, the March equinox becomes the spring equinox (also known as the vernal equinox), the September equinox becomes the fall equinox, the June solstice becomes the summer solstice and the December solstice becomes the winter solstice. EQUATORIAL CHART +60° +30° +60° +30° June Solstice Ecliptic 0° March Equinox September Equinox September Equinox Direction of the Sun's Annual Motion (West to East) -30° -60° 12 h 6 h 0 h December Solstice 18 h 0° -30° 12 -60° h Figure 2-7: The location of equinoxes and solstices.. Fall 2008 Coordinate Systems and Stars 10 V: Exercises Table 1: Coordinates of some sky objects and points on the SC001 Equatorial Chart This first line is filled in as an example. Fill in the missing data in the remaining lines. Object Name Object Type Right Ascension (RA) Declination (Dec) Leo Constellation 10hr 30m +20◦ Constellation 2hr 15m +24◦ Constellation 18hr 30m −30◦ Star 23hr 0m −30◦ Star 6hr 45m −17◦ 6hr 0m +45◦ β Bo¨tis o Star γ Trianguli Star Delphinus Constellation Arcturus Canis Minor M31 Galaxy Star Pleiades Star Cluster Vernal Equinox Sky Point Summer Solstice Sky Point Table 2. Coordinates of some sky objects and points on the SC002 Polar Chart. Object Name Object Type Cassiopeia Constellation Constellation Capella Right Ascension (RA) Declination (Dec) 5hr 30m +40◦ 11hr 5m +62◦ Star Star Thuban Star α Lacerti Star M51 Galaxy North Celestial Pole Sky Point Fall 2008 Coordinate Systems and Stars 11 Find the constellation Orion, along the celestial equator. Find the proper names of the four bright stars whose Greek-generic name is given below. Also give the M (Messier Catalog) number of the Great Nebula in Orion, a gas cloud located just below Orion’s belt, in the position of his sword. α Orionis β Orionis γ Orionis κ Orionis M , The Great Nebula in Orion Due to the Earth’s motion around the Sun, different stars and constellations are visible in the evening sky during the year. Notice the dates along the bottom of the SC001 chart. These dates indicate when the stars above are best viewed at 8PM. ⇒Based on these dates, what is the best month of the year to view the following constellations? Object Declination Month 0◦ Orion The Great Square (in Pegasus) +20◦ Scorpius −30◦ Name four constellations which should be visible in the sky tonight. Choose constellations with brighter stars, making them easier to locate. 1) 2) 3) 4) The hours of right ascension are based on the hourly motion of the stars across the night sky. For example, a star with right ascension of 8 hours rises three hours after a star whose right ascension is 5 hours. At any given time, we have a twelve hour window on the sky. Answer these questions based on the right ascension position of these constellations along the celestial equator. ⇒ What constellation (with roughly the same declination) rises about four hours after Orion? Ans: ⇒ What constellation is rising in the east, as the constellation Ophiuchus is setting in the West? Ans: Fall 2008 Coordinate Systems and Stars 12 VI: Part II - Apparent Magnitude The brightness of a star, as we see it from Earth, is called its apparent magnitude. A magnitude number is assigned to each star based on its brightness, with the dimmer stars having higher numbers. A key to stellar magnitudes used in the charts, is given at the upper left and lower right corners of each chart. It may be easier to use one chart’s key to compare the size of dots on the other chart – or – use a small plastic ruler to measure dot diameter. ⇒Based on the magnitude key, what is the approximate apparent magnitude of the following stars? (Note: It is OK to use 1 magnitudes when you can’t decide which dot size fits best.) 2 Star Approximate Position Sirius 7hr , −15◦ Altair 20hr , +10◦ α Cancri 9hr , +10◦ Canopus Apparent Magnitude 6hr , −53◦ Give the apparent magnitude of each of these stars in the constellation Leo the lion. Some of Leo’s stars are not in the stick figure pattern. In some cases, it may be necessary to estimate the magnitude. Use half magnitudes if you can not decide between two whole magnitudes from the chart scale. Not all of these stars are linked by the stick figure. Alpha, α Delta, δ Eta, η Mu, µ Beta, β Epsilon, ε Theta, θ Omicron, o Gamma, γ Zeta, ζ Lambda, λ Rho, ρ The number of stars visible in the sky depends both on the star magnitudes and the seeing conditions. For instance, more stars are visible in the center of Lake Michigan than in the center of Grand Rapids. Using the magnitude information on the chart for each star in the constellation, count (from the map) the number of visible stars (±2 in the lower magnitudes) in the constellations Orion and Aquarius under the four conditions listed in the table below. The “lowest magnitude” column states the dimmest visible star magnitude under the particular seeing condition. Seeing Condition Lowest Magnitude Top of Parking Ramp 3 Country Field 4 Perfect Aquarius 2 City Backyard Orion 6 Fall 2008 Coordinate Systems and Stars 13 AS103 - Descriptive Astronomy Lab 3: Seasons – Fall 2008 Due Date: Day Performed Name Lecture Section Partner Score / 40 Partner Note1: I will be in the lab classroom to answer your questions while you work on this lab. However, if you ask me a question that makes it appear that you did not read the instructions, all I will tell you is, “go read the instructions...” Note2: Any term shown in bold is a term you are responsible for knowing and could show up on the Unit Test. I: Finding the Altitude of Objects from their Declination In this section we learn three important rules. They are marked in boxes as we discuss the material. These are the rules you will use to solve the upcoming problems in this lab. The Altitude of the Celestial Pole. The north celestial pole has +90◦ declination. This is (very nearly) the location of Polaris, the North Star. When standing on the North Pole, the NCP is at the zenith. When standing on the Earth’s equator, the NCP is on the northern horizon. The altitude of the NCP (and Polaris) is equal to the observer’s latitude. This fact has been used by navigators at sea for centuries. This is rule number 1: Rule 1: The altitude of the NCP (and Polaris) is equal to the observer’s latitude. For observers south of the Earth’s equator, the altitude of Polaris is negative, because it is below the northern horizon. Thus, any southern latitudes, have a negative altitude for Polaris. The south celestial pole has −90◦ declination. When standing on the South Pole, the SCP is at the zenith. (Polaris is on the nadir.) The SCP can never be seen in Grand Rapids, or any other place north of the Earth’s equator. Finding the Altitude of the Celestial Equator. Since the declination of objects is measured from the celestial equator, we must find the celestial equator in our night sky. The celestial equator is a line running from east to west across our southern sky (because we are observing in the northern hemisphere). Since we can not actually see the celestial equator (it’s hard to draw on the sky), we must calculate and mentally picture its position in the sky. We always calculate the altitude of the celestial equator at the point where it crosses our local meridian. Thus, we measure the altitude of the celestial equator from our southern horizon. The altitude of the celestial equator is equal to 90◦ minus the observer’s latitude. This simple relation is due to the north celestial pole and the celestial equator being (by definition) 90◦ apart. Also, the due north and due south horizons are 180◦ apart. Looking at Figure 3-1, we see the altitude of the celestial equator comes from Fall 2008 Seasons 14 Zenith Cel e 47 º 90º West º 43 The altitude of the celestial equator is 90º minus the latitude. st ial Eq ua to r This angle is always 90º Lo c al M eri dia n Polaris This angle is equal to the observer's latitude. North South Observer at 43ºN Horiz on East Figure 3-1: The altitude of the celestial equator in Grand Rapids. ACE = 180◦ − 90◦ − 43◦ = 47◦ Because the celestial equator is always 90◦ from the NCP, and the due north and due south horizons are always 180◦ apart, the 180◦ and 90◦ values are always in the equation, regardless of the observer’s latitude. We can simply do the subtraction of these two numbers to get, ACE = 90◦ − 43◦ = 47◦ Figure 3-1 also shows us that the 43◦ in this equation is simply the altitude of the NCP (or Polaris) as seen from Grand Rapids. This is also the latitude of Grand Rapids (43◦ N). So, for Grand Rapids, the celestial equator is at altitude 90◦ − 43◦ = 47◦ . When given the latitude of a location, find the altitude of the celestial equator with this formula: Rule 2: ACE = 90◦ − Latitude This altitude is always measured off the southern horizon. For observers in the southern hemisphere, the altitude of the celestial equator is calculated the same way as for the northern hemisphere, but the resulting altitude is then measured off the northern horizon rather than the southern. In Grand Rapids, the celestial equator’s altitude is 47◦ above the southern horizon. Any object with declination below −47◦ can not be seen in Grand Rapids anytime of the year. Also, all objects whose declination is greater than +47◦ are circumpolar objects. Miami, Florida is at latitude 26◦N. In Miami, the dotted line from the observer to Polaris, shown in Figure 3-1, would rotate clockwise, as shown in Figure 3-2. The 43◦ angle becomes 26◦ . In Miami, Polaris is at altitude 26◦ in the north and the celestial equator is at altitude 90◦ − 26◦ = 64◦ from the southern horizon. The Earth’s equator is at latitude 0◦ . There, the altitude of Polaris is 0◦ and the altitude of the celestial equator is 90◦ . As promised, the celestial equator is directly overhead when standing on the Earth’s equator. We can look one last place – the North Pole, at latitude 90◦ N. At the North Pole, Polaris is at the zenith (altitude = 90◦ ) and the celestial equator is at altitude 0◦ . So, the celestial equator is right on the horizon (all the way around). On a more practical note, in winter, the celestial equator is found just above Orion’s belt, and in summer, about 10◦ below the southern tip of the Summer Triangle (Altair). Fall 2008 Seasons 15 Zenith Loc t es Ce l al Me rid ian E ial a qu 90º This angle is always 90º to 64 º r West º 26 The altitude of the celestial equator is 90º minus the latitude. Polaris This angle is equal to the observer's latitude. North South Observer at 26ºN Horiz on East Figure 3-2: The altitude of the celestial equator in Miami, Florida. The altitude of a Celestial Object. Given the declination of an object, calculating its altitude as it crosses the local meridian is easy. We have already discussed how to figure out the altitude of the celestial equator on the local meridian. (See rule 2.) Once this is known, finding the altitude of the object as it crosses the local meridian (called the object’s transit altitude or upper culmination ) is simply an addition problem. Calculating the horizon coordinates of an object from its equatorial coordinates is possible, given the time, date and Earth location for the observation. The general form of this calculation is beyond the scope of this course (it involves spherical trigonometry). Rule 3: Aobject = ACE + Decobject In words, rule three says that the altitude of an object as it crosses the local meridian is equal to the altitude of the celestial equator (at the observer’s latitude) plus the declination of the object. In Grand Rapids, the altitude of the celestial equator on the local meridian is +47◦ from the southern horizon. The star, Altair, has a declination coordinate of +9◦ . To find the altitude of Altair when it transits the local meridian, simply add its declination to the altitude of the celestial equator. Thus, Altair crosses the local meridian at +47◦ + 9◦ = +56◦ off the southern horizon. The star, Sirius, has a declination coordinate of −17◦ . Therefore, it transits the local meridian at altitude +47◦ −17◦ = +30◦ from the southern horizon. The bright star Capella is at declination +46◦. In Grand Rapids, this gives a transit altitude of 47◦ + 46◦ = +93◦ for Capella. However, since altitudes are never greater than +90◦ , this result tells us that Capella transits the local meridian at 180◦ − 93◦ = +87◦ off the northern horizon. In the northern hemisphere, Rule 3 always finds the altitude of an object from the southern horizon. If the result of the calculation for Rule 3 is greater the 90◦, then subtract the result from 180◦ and take the altitude measurement from the northern horizon. If you are in the southern hemisphere, the roles of north and south in this statement are reversed. The right ascension of the stars Altair and Sirius are 19h 50m and 6h 45m, respectively. Thus, when Altair transits the local meridian, the sidereal clock reads, 19:50. When Sirius transits the local meridian 10 hours and 55 minutes later, the sidereal clock reads, 6:45. The reading on the solar clock during these events depends on the time zone and date. Fall 2008 Seasons 16 I I: Exercises ⇒Given the following locations and the rules given above, determine the altitude of the celestial pole (north or south) and the celestial equator on the local meridian. For each, specify whether the altitude is measured off the northern or southern horizon. Note : There are special situations where the measurement horizon could be either one, or it can’t be specified because it could be measured from any point on the horizon. Make notes of these special situations below the table. Location Latitude Grand Rapids 43◦ N Miami, Florida 26◦ N Kansas City, Kansas 35◦ N London, England 51◦ N North Pole 90◦ N Equator 0◦ Sydney, Australia 32◦ S Cape Horn, Chile 55◦ S South Pole AltitudeCP N/S AltitudeCE N/S 90◦ S Special notes on horizons: ⇒Now we stay here in Grand Rapids (43◦ N) and observe a few celestial objects. For the objects in the table below, determine their transit altitude on the Grand Rapids local meridian. For each result, state whether the altitude is measured off the northern or southern horizon. Object Right Ascension Declination AltitudeObject Horizon Altair Sirius Capella Polaris Regulus Sagittarius Vernal Equinox Betelgeuse α Centauri Fall 2008 Seasons 17 I II: The Seasons The seasons occur because of two effects – the efficiency with which the Sun heats the earth and the length of the day at the observer’s latitude. Both effects are caused by the tilt of the Earth’s rotational axis and so, the reason we have seasons is that the Earth’s axis of rotation is tilted. Important Dates for Seasons There are four important dates for the seasons of the year. You should know each date and be able to find the position of the Sun on the celestial sphere (its declination) and in the high noon sky (its local meridian transit altitude). The altitude of the Sun at noon depends on your latitude on Earth. We discuss the altitude of the Sun after the description of the general characteristics of each day. Each of the four dates has a name. March 21, is the vernal equinox or spring equinox. June 21, is the summer solstice. September 21, is the autumnal equinox or fall equinox. December 21, is the winter solstice. The Latin word “equinox,” means that on these days, the number of daytime hours and nighttime hours is equal: 12 hours each. The Latin word “solstice” comes from the words Sol and sistere, and means “Sun stand still.” On the solstice days, the Sun reverses its apparent annual north-south motion along the local meridian. You should know the name, the declination and noon altitude of the Sun for each of these four important dates. Use your SC001 Constellation Chart for the following paragraphs. March 21 – The Spring, or Vernal Equinox On March 21, the Sun crosses the celestial equator and is thus directly above the Earth’s equator. The Sun’s declination is 0◦ . This date is often called the first day of spring. On this day the periods of daylight and darkness are equal (12 hours) everywhere on Earth. The Sun rises due east and sets due west. For anyone standing on the Earth’s equator, the Sun rises straight up in the east, crosses the zenith, and sets straight down in the west. For anyone standing on the North Pole (or the South Pole) the Sun circles the sky right along the horizon, never rising or setting for the entire day. June 21 – The Summer Solstice This day is often called the first day of summer. The declination of the Sun is +23.5◦. The Sun is farthest north of the celestial equator. On Earth, the Sun is directly over the Tropic of Cancer, (23.5◦N). The Sun stays at nearly the same declination (and thus, the same altitude) for about two weeks. We have long days and short nights. September 21 – The Fall or Autumnal Equinox The Sun is again directly above the Earth’s equator. This is called the first day of fall. The conditions are the same as described for March 21. The declination of the Sun is 0◦ . December 21 – The Winter Solstice This day is called the first day of winter. The Sun is farthest south of the celestial equator. On Earth, the Sun is directly over the Tropic of Capricorn, (23.5◦S). The declination of the Sun is −23.5◦. We have short days and long nights. Determining the Sun’s Altitude We start with some reminders: Altitude 90◦ is straight up and is called the zenith. Altitude 0◦ is on the horizon. Negative altitudes are below the horizon. The altitude of the Sun at high noon (when it transits the local meridian) depends on your latitude. The altitude can be found for any latitude on any day by following these three steps: 1. Given the latitude, find the altitude of the celestial equator using Rule 2. 2. Given the date, find the declination coordinate of the Sun. This can be found on the SC001 Constellation Chart or, if it is one of the four important dates listed above, you should know the Sun’s declination. 3. Add the Sun’s declination to the altitude of the celestial equator. This is the Sun’s altitude off the southern Fall 2008 Seasons 18 horizon. If it is greater than 90◦ , we must subtract the result from 180◦ to obtain the Sun’s altitude off the northern horizon. (This will not happen within the boundaries of the mainland United States.) In any case, the Sun’s altitude can never be greater than 90◦. Heating the Earth Because of the Sun’s changing declination, the Sun’s altitude on the local meridian varies during the year. This variation of the Sun’s altitude creates its apparent annual north-south motion along the local meridian. Because light carries energy, sunlight warms any surface it strikes. The rate of warming depends on the angle at which the sunlight hits the surface of the object. The warming rate is highest when light hits the surface straight on, at a right angle. As the surface is tilted away from the sunlight, the rate of warming decreases. A thin metal plate held so it casts a thin line shadow on the ground, is not warmed by the Sun. If it is held so it casts a large shadow, it is easily warmed by the sunlight. If we leave the metal plate on the ground for a year, the changing altitude of the Sun has the same effect as changing the tilt of the metal plate to the Sun’s rays. During the summer, sunlight hits the metal plate (and the ground) more directly than during the winter. Like the plate, the earth is warmed in the summer, and allowed to cool in the winter. The Sun’s rays always strike the equatorial regions of the Earth almost straight on. However, at the poles of the Earth, the Sun’s rays always strike the ground at a very shallow angle. The equatorial region is warm and the polar regions are cold because of the angle of the Sun’s rays as they strike the surface of the Earth in those regions. The change in the Sun’s altitude also changes the length of the day. Looking at Figure 3-3 and Figure 3-4, you should see how the sunrise point along the horizon (its azimuth) changes during the year. During the summer (Figure 3-3), the Sun rises in the northeast and sets in the northwest. On an equinox day, the Sun rises due east and sets due west. Finally, during the winter months (Figure 3-4), the Sun rises in the southeast and sets in the southwest. In these figures, the 12-hour circle is drawn from the NCP to the SCP such that it crosses the celestial equator on the observer’s east and west horizons. It always takes the Sun 12 hours to travel from the east side of this circle to the west side, independent of the season. In the summer, the Sun rises before it gets to the 12-hour circle in the east and sets after it crosses the 12-hour circle in the west. Thus, the days are longer than 12 hours. In winter, the Sun crosses the 12-hour circle before it rises and after it sets. Thus, the winter days are shorter than 12 hours. During the summer months, the days are long and the Sun is high in the sky. This combination warms our region of the Earth and causes our long warm summer days. During the winter months, the Sun is low in the southern sky and the days are shorter. This combination creates the cooler weather. Zenith This is the declination of the Sun on the summer solstice Daytime path of the Sun "12 hour Circle" This angle is equal to the latitude 23.5º 70.5º 47º West le Ce 43º ial st This angle is 90º minus the latitude. Loca lM eri dia n Polaris r to ua Eq South North Observer Horiz on East Figure 3-3: The altitude of the Sun on the summer solstice, in Grand Rapids. Fall 2008 Seasons 19 Zenith This is the declination of the Sun on the winter solstice an idi er Daytime path of the Sun "12 hour Circle" Lo ca lM Polaris This angle is equal to the latitude 47º -23.5º This angle is 90º minus the latitude. South r to ua Eq Horiz on l tia les Ce 23.5º West 43º North Observer East Figure 3-4: The altitude of the Sun on the winter solstice, in Grand Rapids. You may have noticed the coldest winter days come about a month after the first day of winter. Also, the warmest days of summer come about a month after the first day of summer. It takes about one month for the cooling or warming process to affect our weather. After all, it takes some time for a pan of water to reach boiling after placing it on the burner. Also, hopefully, you would not place your hand on the burner only one minute after turning it off. In any physical system, it takes time for heat energy to build up, or to dissipate. The Earth’s Axial Tilt Look at your SC001 Constellation Chart. The celestial equator is the straight line across the middle of the map. The 23.5◦ tilt of the Earth’s axis of rotation causes the ecliptic to snake 23.5◦ north and south of the celestial equator which in turn causes the seasonal variation in the Sun’s local meridian (high noon) altitude to an observer on Earth. As the Earth travels around the Sun, it follows an orbital path. Principles of physics require this path to lay in a flat plane, like the surface of a table. Any two objects in orbit around each other must orbit each other in a mathematical plane. The plane passes through the center of both objects. In general, this plane is called an orbital plane and it contains the path of the orbiting body. The Earth’s orbital plane has a special name, it is called the ecliptic plane. We use the ecliptic plane to define “up” and “down” in the solar system. If we are located above the ecliptic plane, then we can look “down” to see the Earth’s north pole. If we are below the ecliptic plane, we can look “up” to see the Earth’s south pole. A line, perpendicular to the ecliptic plane defines the vertical (up and down) direction of the solar system. The 23.5◦ tilt of the Earth is measured with respect to the ecliptic plane’s definition of vertical. This angle is also known as the obliquity of the ecliptic. If the Earth were not tilted on its axis, its axis would be vertical, or perpendicular to the ecliptic plane. The ecliptic line represents the location where the ecliptic plane passes through the celestial sphere. If the Earth were not tilted, the ecliptic line would lie on the celestial equator because the ecliptic plane would pass through the Earth at the Earth’s equator. The Sun would remain on the celestial equator (directly above the Earth’s equator) all year long. The Earth would not have any seasons. Instead, there might be climate zones. However, the Earth’s axis is tilted. The Earth’s axis makes a 23.5◦ angle with the vertical line of the ecliptic plane. Notice (by looking at the SC001 Chart ), the minimum and maximum solar declination is equal to the Earth’s axial tilt. Because of the tilt of the Earth’s rotational axis, the Sun’s altitude on the local meridian varies during the year. This variation of the Sun’s altitude on the local meridian causes increasing or decreasing efficiency in the Sun’s ability to warm the earth. This, along with the variation in the length of daylight also caused by the Earth’s tilt, causes the seasons of the year. The obliquity of the ecliptic is the sole reason for the seasons. Fall 2008 Seasons 20 One thing to be aware of in terms of describing the general character of seasonal days for any given location. That is, local effects of the ocean may cause the character of the seasons for a given place. England has very mild winters compared to the mid-western United States, even though it is at latitudes equivalent to Hudson’s bay. This is caused by the warm ocean currents reaching and surfacing near England. This warm water warms the atmosphere causing England to have the milder winters. Tropics and Circles On the first day of summer, the declination of the Sun is +23.5◦, and the Sun is directly over the Tropic of Cancer. The Tropic of Cancer is a line drawn parallel to the Earth’s equator at latitude 23.5◦N. The Tropic of Capricorn is a line drawn parallel to the Earth’s equator at latitude 23.5◦S. “Tropic” is a Latin word for “turning points.” A few thousand years ago, when these lines were named, the summer solstice occurred when the Sun was in the constellation Cancer, and the winter solstice occurred when the Sun was in Capricornus. Since the Earth’s rotational axis precesses, the summer solstice is now in Gemini and the winter solstice is located in Sagittarius. The Arctic Circle and the Antarctic Circle are located at 66.5◦N and 66.5◦S, respectively. The Arctic Circle designates the latitude above which the Sun never sets during the summer solstice. This has also been called “the land of the midnight Sun.” During the winter solstice, this same region is in 24 hours of darkness. The Antarctic Circle represents the same events for the south polar regions. IV: Exercises ⇒For the following places, determine the noon altitude of the Sun on the important season dates. Location Latitude Grand Rapids 43◦ N Miami, Florida 26◦ N Kansas City, Kansas 35◦ N London, England 51◦ N Equator Equinox Days Summer Solstice Winter Solstice 0◦ ⇒ Based simply on latitude and ignoring any local environmental effects, which of these locations should have the coldest winter weather? Ans: Fall 2008 Seasons 21 ⇒ Think carefully about Figure 3-2 and the 12-hour circle within it. Compared to the azimuth of sunrise on the summer solstice in Grand Rapids, would you expect the azimuth of summer solstice sunrise in Miami to be farther north than in Grand Rapids, or closer to due east than in Grand Rapids? Hint : Think about the daily path of the Sun across the sky when you’re standing on the Arctic Circle, compared to Grand Rapids. Explain your answer. Ans: ⇒ Using your new knowledge of what happens to the NCP (and Polaris) as you move farther south in latitude, combined with the 12-hour circle of Figure 3-2, how long would you expect daylight to last for someone living at the Earth’s equator, on the summer solstice? Why? Would it be any different on the winter solstice? Ans: Fall 2008 Seasons 22 AS103 - Descriptive Astronomy Lab 4: Motion of the Sun and Lunar Phases – Fall 2008 Due Date: Day Performed Name Lecture Section Partner Score / 40 Partner Note1: I will be in the lab classroom to answer your questions while you work on this lab. However, if you ask me a question that makes it appear that you did not read the instructions, all I will tell you is, “go read the instructions...” Note2: Any term shown in bold is a term you are responsible for knowing and could show up on the Unit Test. I: Part I - The Motion of the Sun The curved line which snakes across the SC001 chart, marks the apparent path of the Sun as it moves among the stars during the year. This path is known as the ecliptic line and it crosses the celestial equator at the equinox points. The dates given along this line indicate when the Sun occupies that position. The degree numbers just above the ecliptic line give the Sun’s celestial longitude (ecliptic coordinate system, symbol: λ “lambda”). ⇒Determine the Sun’s right ascension and celestial longitude (λ) position on the dates listed in the table below. Be careful not to confuse celestial longitude degrees with declination degrees. Date Sun’s RA (hr, min) Celestial Longitude (Degrees) Vernal Equinox Autumnal Equinox February 20 October 7 The constellations which the Sun passes through are known as the zodiac constellations. ⇒In which zodiac constellation is the Sun located on these days? Nov. 18 April 12 ⇒According to astrology, what is your zodiac sign? Fall 2008 Motion of the Sun and Lunar Phases 23 ⇒ Does this agree with the actual position of the Sun on your birthday? Explain the cause of any difference between the constellations and the zodiac signs (whether yours is different or not). (Hint : It is due to one of the Earth’s three motions studied in chapter 2.) Ans: ⇒What constellation does the Sun occupy on December 12? As the Sun moves among the stars, its declination changes. This causes it to appear higher or lower in the sky at different times of the year. Our seasons are related to these changes in position. ⇒Using what you learned in the previous lab, what is the declination of the Sun on these dates? Winter Solstice Summer Solstice ◦ The latitude of Grand Rapids is 43 N. This means in Grand Rapids, the altitude of the celestial equator as it crosses the local meridian is 90◦ − 43◦ = 47◦. The altitude of any object (including the Sun) as it crosses the local meridian is equal to the altitude of the celestial equator plus the declination of the object. For the Sun, this is also called the noon altitude. ⇒What is the noon altitude of the Sun in Grand Rapids when it is located at the winter and summer solstices? Summer Solstice Winter Solstice June 21st and December 21st are known as the solstices because the Sun stays at the same noon altitude for several days. Compare the change in altitude of the Sun in Grand Rapids during late June to that during late March by completing this chart. A solstice occurs when the Sun’s altitude does not change. (Beware: because we are working with low resolution maps, we might see a small change in the altitude of the Sun when there really shouldn’t be.) Calculating the noon altitude is exactly the calculation you just did to answer the questions above. After calculating the noon altitude for a pair of dates, calculate the change in altitude between the dates. This change in altitude determines weather the Sun has passed through a solstice. Date Declination (x◦) Noon Altitude (x◦) Change in Altitude (x◦) Solstice? (Y/N) March 5 April 5 June 5 July 5 II: Part II - Lunar Phases The Moon’s orbital path lies very near the ecliptic line. For the purposes of this lab, we’ll consider the Moon’s path to be the same as the ecliptic line. While the Sun requires a year to complete one trip along the ecliptic, the Moon requires only one month, or 29.5 days. As the Moon moves along the ecliptic during its cycle, it goes through a sequence of phases. The lunar phase depends on its location relative to the Sun. Figure 4-1 shows the Sun at its position for March 21 (spring equinox) and the position of the Moon for each of its possible phases on that date. During the year, the Sun moves to the left, and the position of each of the possible lunar phases shifts to the left in step with the Sun. Fall 2008 Motion of the Sun and Lunar Phases 24 SC001 Constellation Chart first quarter l=135° waxing gibbous waxing crescent l=90° l=0° (l=360°) Sun l=45° new moon (In same place as the Sun) full moon l=180° l=315° l=270° waning crescent 12h 9h 6h 3h 0h l=180° full moon Celestial Equator 21h l=225° third quarter 18h 15h waning gibbous 12h Figure 4-1: Moon phase positions, 1. The table below shows a quantity called the lunar phase angle, which we give the symbol φ (pronounced, “fee”). The lunar phase angle is calculated by subtracting the celestial longitude of the Sun from the celestial longitude of the Moon. That is, φ = λM oon − λSun . Note that λ = 0◦ is the same as λ = 360◦. Compare phi in this table with phi in Figure 4-4. Hints : Angles measured counter-clockwise (from the Sun, at new Moon position, φ) on Figure 4-4 are equivalent to celestial longitude angles measured to the left, from the Sun’s position, along the ecliptic line of the equatorial chart. That is, the angles shown with the Moon’s position in Figure 4-4 represent the difference in the Sun’s and Moon’s celestial longitude. The Sun’s celestial longitude is directly related to the date. The Moon’s phase is related to the difference in the Sun’s and Moon’s celestial longitude (φ) and that relation is shown by Figure 4-4. When Figure 4-4 says that the Moon’s position is φ = 90◦, it’s saying that the difference between the position of the Sun and the Moon is 90◦ , with the Moon on the left side of the Sun’s position. (Remember also that the map wraps around.) Phase φ (◦ ) Phase φ (◦ ) New Moon 0◦ − 0◦ = 0◦ Full Moon 180◦ − 0◦ = 180◦ Waxing Crescent 45◦ − 0◦ = 45◦ Waning Gibbous 225◦ − 0◦ = 225◦ First Quarter 90◦ − 0◦ = 90◦ Third Quarter 270◦ − 0◦ = 270◦ Waxing Gibbous 135◦ − 0◦ = 135◦ Waning Crescent 315◦ − 0◦ = 315◦ As the Sun moves along the ecliptic line, the phases of the Moon shift by a proportional amount (see Figure 4-2). Fall 2008 Motion of the Sun and Lunar Phases 25 SC001 Constellation Chart first quarter l=135° waxing crescent l=90° new moon (In same place as the Sun) waning crescent Sun l=45° waxing gibbous l=180° Celestial Equator l=0° (l=360°) l=270° third quarter l=315° 12h 9h 6h 3h 0h waxing gibbous l=180° 21h waning gibbous 18h l=225° full moon 15h 12h Figure 4-2: Moon phase positions, 2. Now the phase angle table becomes (compare φ in this table with φ in Figure 4-4): Phase φ (◦ ) Phase φ (◦ ) New Moon 45◦ − 45◦ = 0◦ Full Moon 225◦ − 45◦ = 180◦ Waxing Crescent 90◦ − 45◦ = 45◦ Waning Gibbous 270◦ − 45◦ = 225◦ First Quarter 135◦ − 45◦ = 90◦ Third Quarter 315◦ − 45◦ = 270◦ Waxing Gibbous 180◦ − 45◦ = 135◦ Waning Crescent 360◦ − 45◦ = 315◦ Use Figure 4-1 and Figure 4-2 with the SC001 chart to determine the location of the Moon during these phases on June 21 (summer solstice) shown in Figure 4-3. Remember the SC001 chart wraps around on its left/right edges. For all these phases, the Sun remains in the same position, because we are interested in the position of the Moon for each phase on this particular date. Fill in the drawing of Figure 4-3 by shading in the unlit portion of the Moon for each phase, and label the phase with its name and its celestial longitude. Your completed drawing should look similar to figures 1 and 2, noting the change in the position of the Sun. Fall 2008 Motion of the Sun and Lunar Phases 26 SC001 Constellation Chart Sun Celestial Equator 12h 9h 6h 3h 0h 18h 21h 15h 12h Figure 4-3: Your drawing of the next step in the Moon phase position sequence.. ⇒Using the chart you just drew as Figure 4-3 and also using Figure 4-4 as guides, fill in the following table. Find the name the zodiac constellation at the Moon’s location by looking at the SC001 chart). One added little twist here is that we will measure the phase angle in hours rather than degrees. The concept is exactly the same as before, we’ve just changed the units of measure. Moon Phase Sun RA (hr) New 6hr Waxing Crescent 6hr First Quarter 6hr Waxing Gibbous 6hr Full 6hr Waning Gibbous 6hr Third Quarter 6hr Waning Crescent 6hr Fall 2008 Moon RA (hr) φ (hr) Zodiac Constellation Motion of the Sun and Lunar Phases 27 ⇒Use your problem solving skills to complete the following table. This time the Sun will be in different locations and we’re working with the Sun’s and Moon’s celestial longitude (λ) measured in degrees, as marked off along the ecliptic line. The first line of the table is shown as an example. For “Today” use today’s date with the current lunar phase (probably written on the chalkboard). It may help to use Figure 4-4 for this exercise. Date Sun λ Moon λ φ (◦ ) Phase March 21 0◦ 180◦ 180◦ Full June 21 Full 237◦ 311◦ New 131◦ Sept 22 First Quarter 20◦ May 11 142◦ 232◦ “Today” ⇒In what constellation is the Full Moon located on these dates? February 15 October 22 ⇒On what day of the year is the Full Moon seen highest in the midnight sky? ⇒If a total lunar eclipse happens when the Moon is at 250◦, what is the date? Fall 2008 Motion of the Sun and Lunar Phases 28 Figure 4-4: The orbital position of the Moon for its phases. Third Quarter Motion of the Sun and Lunar Phases Waning Crescent Waxing Gibbous 181º < f < 269º Waning Gibbous Sunrise Third (Last) Quarter Noon Rotation of Earth First Quarter Sunset f = 90º f = 270º Midnight 91º < f < 179º Waxing Gibbous Full Moon f = 180º Waning Gibbous Full Moon First Quarter Waxing Crescent New Moon New Moon (Not Visible) f = 0º Waning Crescent 271º < f < 359º f Orbital Motion of the Moon Waxing Crescent 1º < f < 89º Gibbous Phases - Crescent Phases More than Half Lit Less than Half Lit Earth Fall 2008 29 Sunlight Waning Phases Left Side Lit Waxing Phases Right Side Lit Sunlight AS103 - Descriptive Astronomy Lab 5: Atomic Spectra – Fall 2008 Due Date: Day Performed Name Lecture Section Partner Score / 40 Partner I: Equipment Each station must have the following: (one of each item) AC Lamp Power Supply Long Filament Lamp Spectrum Tube Power Supply Atomic Spectra Tube (selected Blue Filter Red Filter Yellow Filter from: H, He, N, Ne, Hg, Ar) Diffraction Grating (5000 lpi) Table Lamp Holder Hand-Held Spectrometer II: Introductory Concepts Energy changes within atoms and molecules result in the emission or absorption of bundles of light energy called photons. Photons of certain energies (frequencies or wavelengths) react with our eyes and produce the sensation we call light. A spectroscope is used to distinguish and separate photons, based on their energy (or color or wavelength). In this experiment, a small, hand-held spectroscope is used to examine the spectrum of visible light from various light sources. The filament of the light bulb, or the gas within the spectrum tube, is heated by an electric current to a high temperature so that it emits light. Because the bulb filament is a black body (or thermal) radiator producing a continuous spectrum, we can see a relationship between the temperature of the light bulb filament to its color and brightness. This is the first part of the experiment. The second half of the experiment looks at the spectrum of the filament. The spectroscope is used to split the light into its spectrum, so we can analyze the light emitted by the light bulb or gaseous chemical element. The appearance of the spectrum depends on how the photons were created. In general, spectra can be divided into six types, as shown in Figure 5-1. In most cases, this experiment presents emission spectra, because we are using light bulbs and chemical element spectra tubes, all of which emit light. If a material (like a filter) is placed between the light source and the diffraction grating, then the spectrum becomes the absorption spectrum of the material rather than the emission spectrum of the light bulb. Filters absorb a wide band of colors from the spectrum rather than a narrow line. Fall 2008 Atomic Spectra 30 Absorption Spectra (Energy is absorbed by substance) Emission Spectra (Energy is emitted by source) A D Continuous violet Full, visible spectrum. B violet Bright bands of light against a dark background red C violet Bright lines against a dark background. No visible spectrum. (No light at all.) red red Band -orMolecular Line -orAtomic E violet Dark bands against a bright background. red F violet Dark lines against a bright background. red Figure 5-1: Types of Spectra. III: Part A: Relation of Color to Energy. Plug the single-filament lamp into the variable AC voltage supply (beige power supply), which is then plugged into the lab table’s 120V outlet strip on its side. Make sure the power supply voltage is set to zero, then switch the power supply on. Gradually turn up the voltage on the power supply. The light bulb’s filament should change colors as it gradually gets hotter and brighter. Record the filament color and relative brightness (using words like, “very dim,” “brighter,” etc...) for the voltage ranges shown in the table. DO NOT EXCEED 120 VOLTS! Voltage 20 30 60 120 Color Brightness Based on the above observations, rate these colors from 1 to 5 according to highest (1) to lowest (5) in energy. Color Orange Rank Color Red Rank Color Rank Blue Color Yellow Rank Color Rank White ⇒ If the voltage could be turned up to 500 volts without burning out the lamp, what color would you expect the filament to appear? Ans: Fall 2008 Atomic Spectra 31 IV: Part B: Using the Hand-Held Spectroscope. On your table, you should find a diffraction grating (clear while slide). Hold this grating in front of your eye while looking at the light bulb. You should see the seven colors of the rainbow. Diffraction (a property of all waves) gratings have replaced prisms in the equipment used on telescopes because they present a lower loss in light energy. The hand-held spectrometer (the triangular black, plastic box) contains one of these diffraction gratings at the eye-hole (at the narrow end of the spectrometer). The light enters the spectrometer through a narrow slit (at the wide end of the spectrometer) and passes through the diffraction grating. The light is split into the spectrum and enters your eye, giving the appearance of the spectrum over the wavelength indicator inside the spectrometer. The wavelength indicator is back lit either by the light source in the case of the light bulb, or by using a small flashlight while looking at the dimmer spectral tubes, later in this experiment. There is no visible light to the right of the red, or to the left of the violet. V: Part C: Black Body and Filter Spectra Each person should observe the spectrum produced in each step and record the observation on the figure showing the wavelength indicator inside the hand-held spectroscope. The lamp power supply should be set to about 60 volts (half maximum brightness). ⇒ By selecting a letter (A – F) from Figure 5-1, which of the types of spectra is seen in the hand-held spectrometer when looking at the light bulb? Ans: Notice where the spectrum seems to fade away at each end. Record these positions as vertical dotted lines on the chart below. Also place these dotted lines on the other blank charts in the remainder on the lab. 4 5 6 7 Notice the position of the reddest red, bluest blue, greenest green, and yellowest yellow. Record these in the chart by writing the color name at the approximate position. 4 5 6 7 VI: Part D: The Absorption of Light by Filters Before you place the red filter in the light path, predict which color(s) of the spectrum will be absorbed by the filter. Write your prediction here: Fall 2008 Atomic Spectra 32 Place the red filter in front of the spectrometer slit. Record what you see in the chart below. By comparing what you see here with the spectrum observed in step C2, show the absorbed portion of the spectrum by shading in in the appropriate area. 4 5 6 7 Now predict the color(s) of the spectrum absorbed by the blue filter. Now replace the red filter with the blue filter. Shade in the absorbed portion of the spectrum. 4 5 6 7 Based on the red and blue filter observations, predict which part(s) of the spectrum will be absorbed if the two filters (red and blue) are used together. Try it and describe the results. Explain this result. Now predict the effects of a yellow filter. Place the yellow filter in the light path. Shade in the absorbed regions. 4 5 6 7 ⇒ By selecting a letter (A – F) from Figure 5-1, which type of spectrum do these filters produce? (Hint : The answer is in the “Introductory Concepts” section that you didn’t read.) Ans: Fall 2008 Atomic Spectra 33 VII: Part E: Fingerprint Spectra. Now we look at the emission spectrum from a chemical element. There are six spectral tubes on the counter tops on the north and south sides of the room. Each tube contains a gas of a certain type of atom or molecule. Figure 5-2 shows a map of the room with the tables. Look at this map to determine which of the spectral tubes is “your” element. On top of the spectral tube power supply, there is a small paper “tent” showing the element in the tube. Argon Mercury Helium Neon Hydrogen Nitrogen Figure 5-2: Room map showing spectral tubes assigned to tables.. What chemical element is in your lamp? By selecting a letter (A – F) from Figure 5-1, what type of spectrum does this element produce? Describe the general appearance of your spectrum. Fall 2008 Atomic Spectra 34 Wander around the room to the other tubes and observe the spectrum of each gas. Based on your observations, complete this matching quiz. There are hints in the descriptions. 1. Contains mostly red and orange lines, this is a strong sign. 2. This airy element shows mostly band emissions – as a great many green, yellow and blue lines packed close together. 3. The most abundant element shows both line and band emissions, mostly in the red region. 4. This sad colored element’s spectrum shows bright individual lines of yellow, green and blue. There is very little red. A) Helium B) Nitrogen C) Mercury D) Neon E) Hydrogen F) Argon 5. The tube itself appears white, and the spectrum includes bright lines of red, yellow, green and blue (with other colors). 6. This noble element’s faint spectrum is almost a continuous green and blue with very little, if any, red. Fall 2008 Atomic Spectra 35 AS103 - Descriptive Astronomy Lab 6: Constellation Slides – Fall 2008 Due Date: This lab in not turned in – use it for your reference. Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 36 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 37 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 38 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 39 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 40 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 41 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 42 Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Constellation: Representation 1: Representation 2: Star 1: Star 2: Asterism: Notes: Fall 2008 Constellation Slides 43 AS103 - Descriptive Astronomy Lab 7: Constellation Slides – Cross Reference Guide – Fall 2008 Here is a complete list of the lab final objects, in alphabetical order. Constellations, stars and asterisms for the lab final exam. Constellation Andromeda Aquarius Aquila Aries Auriga Bo¨tes o Cancer Canis Major Canis Minor Capricornus Cassiopeia Cepheus Corona Borealis Cygnus Draco Gemini Hercules Leo Libra Lyra Orion Perseus Pegasus Pisces Sagittarius Scorpius Taurus Ursa Major Ursa Minor Virgo Fall 2008 Representation(s) The Chained Lady, The Princess The Water Bearer The Eagle The Ram The Charioteer The Herdsman The Crab The Big Dog The Little Dog The Goat, The Sea-Goat The Queen The King, The Ethiopian King The Northern Crown The Swan The Dragon, Draco The Twins The Warrior, Hercules The Lion The Scales, The Scales of Justice The Harp, The Lyre The Hunter, Orion The Hero, Perseus The Flying Horse, The Winged Horse The Two Fish, The Fish The Archer The Scorpion The Bull The Big Bear The Little Bear The Goddess of Justice, The Virgin Star(s) Asterism The Water Jug Altair Capella The Kids The Kite Sirius Procyon Albireo, Deneb The Northern Cross Castor, Pollux Regulus The Sickle Vega Betelgeuse, Rigel Algol The Belt The Great Square The Circlet The Teapot Antares Aldebaran Mizar, Alcor Polaris Spica The The The The Constellation Slides – Cross Reference Guide Pleiades Big Dipper Little Dipper Wineglass 44 The tables below are cross reference tables listing constellation representations, stars and asterisms in alphabetical order, then matched to their respective constellation. Table 1: Constellation Representation matched to Constellation: Representation The Archer The Big Bear The Big Dog The Bull The Chained Lady The Charioteer The Crab The Dragon The Eagle The Ethiopian King The Flying Horse The Goat The Goddess of Justice The Harp The Herdsman The Hero The Hunter The King The Lion Constellation Sagittarius Ursa Major Canis Major Taurus Andromeda Auriga Cancer Draco Aquila Cepheus Pegasus Capricornus Virgo Lyra Bo¨tes o Perseus Orion Cepheus Leo Representation The Little Bear The Little Dog The Lyre The Northern Crown The Princess The Queen The Ram The Scales The Scales of Justice The Scorpion The Sea-Goat The Swan The Twins The Two Fish The Virgin The Warrior The Water Bearer The Winged Horse Constellation Ursa Minor Canis Minor Lyra Corona Borealis Andromeda Cassiopeia Aries Libra Libra Scorpius Capricornus Cygnus Gemini Pisces Virgo Hercules Aquarius Pegasus Table 2: Star matched to Constellation: Star Albireo Alcor Aldebaran Algol Altair Antares Arcturus Betelgeuse Capella Castor Constellation Cygnus Ursa Major Taurus Perseus Aquila Scorpius Bo¨tes o Orion Auriga Gemini Star Deneb Mizar Polaris Pollux Procyon Regulus Rigel Sirius Spica Vega Constellation Cygnus Ursa Major Ursa Minor Gemini Canis Minor Leo Orion Canis Major Virgo Lyra Table 3: Asterism matched to Constellation: Asterism The Belt The Big Dipper The Circlet The Great Square The Kids The Kite The Little Dipper Fall 2008 Constellation Orion Ursa Major Pisces Pegasus Auriga Bo¨tes o Ursa Minor Asterism The Northern Cross The Pleiades The Sickle The Teapot The Water Jug The Wineglass Constellation Cygnus Taurus Leo Sagittarius Aquarius Virgo Constellation Slides – Cross Reference Guide 45 AS103 - Descriptive Astronomy Lab 8: Chaffee Planetarium Visit – Fall 2008 Due Date: Day of Planetarium Visit Name Lecture Section Score / 20 I: Procedure We will spend one lab class at the Roger B. Chaffee Planetarium located in the Grand Rapids Public Museum. There is no charge for admission. You must sign the attendance sheet at the end of the show. No credit is given without your initials on the attendance sheet. After the sky motion session, we will watch a regular public show presented by the planetarium. A map showing the location of the planetarium is on the back of this form. II: Show Times Show time is during a regular lab session and is shown on the Semester Schedule document. Information Show Title: Write a brief description of the show. Describe your reaction to the show. (Did you like it? Would you see another?) Fall 2008 Chaffee Planetarium Visit 46 Bridge Street Ford Museum Michigan Street TL Lyon Street Amway Grand Planetarium TL TL Pearl Street TL TL GRCC Days Inn Parking GVSU Public Museum Fulton Street Division TL ive dR r an Gr US 131 Fall 2008 Chaffee Planetarium Visit 47 AS103 - Descriptive Astronomy Lab 9: James C. Veen Observatory Visit – Fall 2008 I: Information The class visit to the James C. Veen observatory is by courtesy of the Grand Rapids Amateur Astronomical Association. The class will observe the rules, regulations and guidelines established by this organization while visiting their observatory. 1. Park in the lower parking lot (located on the right side of the entrance road, before the main entrance gate) and walk up the hill. The only allowed exception for this is any illness that is causing a disability to walk up the hill. Please notify your instructor if you have such a disability. 2. If you have such a disability and drive up the hill, do not use car headlights while on the observatory road. 3. Do not leave the observatory grounds by walking into the surrounding woods or fields – stay on the property. 4. No smoking is allowed anywhere on the observatory grounds. 5. No alcoholic beverages are allowed on the observatory grounds. The visiting schedule is shown on the Semester Schedule document, but the date shown there is tentative and must be confirmed. There are two Sunday nights scheduled (only because is the night of the week when the fewest number of people have to work). If the night is cloudy, we will use the alternate date. If the alternate date is also cloudy, we are out of luck. Arrive at the observatory at the prescribed time (usually, around sunset). General observing can not begin until at least 30 to 45 minutes after sunset. There is a short video presentation showing the history of the observatory, a description of its equipment and its uses. After twilight has passed (generally, about 45-60 minutes after sunset), we begin observing with the 16 inch and 17 inch telescopes. When you visit the observatory you must dress warm, preferably in layers, like a skier. Even when the days are warm, the nights get cold and the observatory is not heated since the domes are open. DO NOT WEAR SHORTS! Bring your sky maps and a SMALL, DIM (preferably red-tinted) flashlight. DO NOT bring a mag-light! The observatory is located about 1/4 mile north of 36th street on Kissing Rock Road. (3308 Kissing Rock Road.) Take Cascade Ave to 36th street. The southeast corner of 36th and Cascade has a large Presbyterian Church. Go east on 36th (it’s the only way you can go) for about 4.5 miles. There is a stop sign at Buttrick Avenue and at Snow Avenue along the way. When you get to Snow Avenue, you have about 1.5 miles to get to Kissing Rock road. Turn left (north) at Kissing Rock (gravel road, north is the only way you can turn). At the bottom of a large hill, you will see a mailbox with a (not necessarily easy to see) five inch, white star on it. (There should also be a white/blue sign at the road, beside the driveway – if I remember to put it there.) The mailbox also has a green house number (3308) sign attached to back edge of its post. This marks the entrance to the observatory. Pull into the observatory road, and follow the road to the parking lot located on your right, before you get to the observatory entrance gate. The road up the hill to the observatory is lit and you should have no trouble following it to the building. (More information can be found at http://www.graaa.org) II: Credit All telescopic observations are extra credit. This is one of the few allowed opportunities for extra credit in the course. Attendance and telescope observation sheets are distributed at the observatory and must be turned in to the instructor at the observatory, that night. No extra credit telescope observation sheets are accepted late (the next day or later). Fall 2008 James C. Veen Observatory Visit 48 de Casca Lake Snow 36th Street Butrick 28th Street 1.5 Mi Kissing Rock Grand River Ave Observatory Parking above gate Parking below gate Presbyterian Church To GR Cascade I-96 To Lansing Two lane road Four/Five lane road Gravel road Stop signs Fall 2008 Whittneyville Road James C. Veen Observatory Visit 49 ...
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This note was uploaded on 01/31/2010 for the course AS 103 taught by Professor Millar during the Fall '08 term at Grand Rapids Community College.

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